1. Field of the Invention
The present invention relates to an interferometer for measuring an aspherical shape by the use of computer generated hologram.
2. Description of the Prior Art
In the measurement of aspherical shape using the computer generated hologram, it is customary that an aspherical surface to be measured is disposed at such a position as the wave face of aspherical wave entering thereonto coincides with the spherical surface approximating to the aspherical surface. In such an arrangement, the spatial frequency of the hologram becomes minimum. Consequently, the preparation of hologram can be easily made without requiring an increased accuracy with respect to the position at which the hologram is formed.
Generally, when an aspherical surface to be examined is determined, only a single position conjugate with that aspherical surface can be determined. In order to reduce the error of the computer generated hologram with respect to its position as small as possible, which error highly affects the accuracy of measurement relating to the aspherical surface, the position of the set hologram must be varied for the conjugate position which is changed in each time when the aspherical surfaces to be measured is changed from one to another. However, this is very difficult to be done actually. In the past, an exclusive interferometer was assembled for each change in the aspherical surface to be measured while the hologram remained set as it is.
Such a measuring process is very inefficient as the kinds of aspherical surfaces to be checked increase. It is thus desirable to use a single interferometer which can measure plural kinds of aspherical surfaces. In such a case, a hologram holder for holding the computer generated hologram as a primary standard is maintained stationary to secure the severe accuracy relating to the position of the hologram. In such an arrangement, it will not be impossible to perform the measurement although the conjugate relationship between the aspherical surface to be measured and the hologram will be disturbed.
However, such an arrangement raises various problems as listed below.
First, as seen from the flow chart in FIG. 3, the preparation of computer generated hologram requires to calculate an approximation from a polynominal for the wave surface of an object as one step in the process. The object wave surface on a hologram which is a wave surface reflected by an aspherical surface to be measured will have a strain created due to the non-conjugation in the aforementioned arrangement. Therefore, the accuracy of the functional approximation in the object wave surface, which is required to prepare the computer generated hologram will be reduced. As a result, the accuracy of measurement for the aspherical shape will also be decreased.
Although the computer generated hologram includes a pattern drawn based on interference fringes corresponding to a different between an aspherical surface to be measured and an ideal aspherical surface, such a pattern represents the components of the aspherical surface included in the object wave surface. If the term "spatial frequency" is now defined as one corresponding to the spacing between the interference fringes which is formed in the computer generated hologram by the object and reference lights, the spatial frequency in the computer generated hologram will be caused to have an upper limit depending on the conditions in the preparation of hologram. Accordingly, the measurable amount of the aspherical components will also be caused to have its upper limit.
The distortion on the wave surface, which is created due to the fact that the computer generated hologram is not in the conjugate position, is considered to be the actually aspherical component in the object wave surface on the hologram. Therefore, the measurable amount of aspherical surface will be reduced corresponding to the distortion in the wave surface, as compared with such an arrangement in which the hologram is in its conjugate position. This measurable amount of aspherical surface greatly varies depending on whether the computer generated hologram is in conjugation with convex or concave surface to be measured.
If a convex surface to be examined rather than a concave surface to be examined is to be measured by positioning the hologram at a location conjugate with the concave surface, therefore, the measurable amount of aspherical surface in the convex surface will be highly limited.
If the computer generated hologram is not disposed at a position conjugate with a surface to be examined, a pattern of interference fringes created from such an arrangement will have a distortion. It thus becomes difficult that each point in the pattern of fringes coincides with the corresponding point on the surface to be examined.
FIG. 4 shows interference fringes obtained by the conventional interferometer which has adopted such an arrangement that the computer generated hologram is not fixed in a position conjugate with a surface to be examined. As seen from FIG. 4, the surface to be examined is in the shape of an aspherical surface which is cut into the rectangular configuration. Due to this arrangement in which the hologram cannot be disposed at the position conjugate with the surface to be examined, it is recognized that the resulting pattern of interference fringes is distorted into a pin-cushion configuration.
Japanese Patent Disclosure No. 63-61925 describes a method and apparatus for analyzing interference fringes in a holographic interferometer which can determine a difference between the actual form and the ideal form in an object to be examined even if there is any error with respect to the arrangement of the object to be examined or the primary hologram standard. In the Japanese Patent Disclosure, only seven coefficients are required to analyze the interference fringes if the hologram is in conjugation with the surface to be examined. On the contrary, thirteen coefficients must be determined if the hologram is not in conjugation with the surface to be examined. Time required to determine such thirteen coefficients becomes huge.